School of Mathematics and Statistics (SoMaS)

MAS241 Mathematics II (Electrical)

Prerequisites: MAS156 (Mathematics (Electrical and Aerospace))

The following modules have this module as a prerequisite:

Aims

• To consolidate previous mathematical knowledge.
• To develop the mathematical techniques used in second year electrical and aeronautical engineering courses.
• To lay the foundations for the study of vector calculus.

Learning outcomes

• Ability to understand complex valued functions, and functions of a complex variable.
• Ability to compute Laplace and Fourier transforms and apply the Laplace transform to solve differential equations.
• Ability to compute Fourier series, and Fourier sine and cosine series.
• Ability to find partial and directional derivatives.
• Ability to apply the chain rule to functions of multiple variables.
• Ability to find critical points of a function of two variables and determine their nature.
• Ability to compute double and triple integrals directly and/or by changing the order of integration/changing variables.
• Ability to compute the gradient of a scalar field, understand and apply its geometric interpretation.
• Ability to compute divergence and curl of a vector field.

Assessment

One formal 2 hour written examination.

Full syllabus

Basics

Review of complex numbers and complex valued functions

Transforms

Important real valued functions including the Heaviside, unit impluse and delta functions; complex Laplace transform and its properties; convolution; applications of the Laplace transform; the Fourier transform and its properties.

Fourier series

Periodic functions; Fourier series; even and odd functions; Fourier cosine and sine series; complex exponential Fourier series.

Functions of several variables

Review of partial derivatives; directional derivatives; chain rule; gradient vector and its geometric interpretation; higher order derivatives and equality of mixed derivatives; determining the nature of critical points for functions of two variables.

Integration

The definite integral; double and triple integrals, their geometric interpretations and properties; change of order of integration; change of variables; surface areas; cylindrical and spherical polar coordinates.

Vector fields

Vector and scalar fields; divergence and curl; elementary properties of divergence and curl.

Reading list